Let's analyze the graph and fill out the description step by step. --- ## Step-by-Step Solution ### 1. **Shape** - The graph shown is a **curve** (already filled). ### 2. **Line of Symmetry** - The graph does **not** appear to be symmetric about any vertical line. - **Answer:** None (already filled). ### 3. **Increasing or Decreasing or Both** - The graph first **decreases** (from left to the minimum) and then **increases** (from the minimum to the right). - **Answer:** Both ### 4. **Asymptotes** - There are **no asymptotes** shown in the graph. - **Answer:** None ### 5. **Intercepts** - **x-intercepts**: Points where the graph crosses the x-axis. - At \( x = -2 \) and \( x = 0 \). - So, the x-intercepts are \( (-2, 0) \) and \( (0, 0) \). - **y-intercept**: Where the graph crosses the y-axis. - At \( (0, 0) \). - **Answer:** (-2, 0), (0, 0) ### 6. **Domain** - The graph has arrows on both ends, so it continues forever in both directions. - **Domain:** All real numbers, or \( (-\infty, \infty) \) ### 7. **Range** - The lowest y-value on the graph is \( y = -2 \), and the graph goes up forever. - **Range:** \( y \geq -2 \), or \( [-2, \infty) \) ### 8. **Continuous or Discrete** - The curve is unbroken. - **Answer:** Continuous ### 9. **Function or Not a Function** - Each x-value has only one y-value. - **Answer:** Function --- ## **Complete Description** | Property | Answer | |-------------------------|---------------------------------| | Shape | Curve | | Line of Symmetry | None | | Increasing/Decreasing | Both | | Asymptotes | None | | Intercepts | (-2, 0), (0, 0) | | Domain | \( (-\infty, \infty) \) | | Range | \( [-2, \infty) \) | | Continuous/Discrete | Continuous | | Function/Not a function | Function | --- ### **Final Answers (for Writing on Worksheet)** - **Shape:** Curve - **Line of symmetry:** None - **Increasing or decreasing or both:** Both - **Asymptotes:** None - **Intercepts:** (-2, 0), (0, 0) - **Domain:** \( (-\infty, \infty) \) - **Range:** \( [-2, \infty) \) - **Continuous or discrete:** Continuous - **Function or not a function:** Function --- **Let me know if you need further explanation or a rewritten version!**

# Step-by-Step Solution ## 1. Shape - The graph shown is a **curve**. ## 2. Line of Symmetry - The graph does **not** exhibit symmetry about any vertical line. - **Answer:** None. ## 3. Increasing or Decreasing or Both - The graph **decreases** initially (from the left to the minimum point) and then **increases** (from the minimum point to the right). - **Answer:** Both. ## 4. Asymptotes - There are **no asymptotes** present in the graph. - **Answer:** None. ## 5. Intercepts - **x-intercepts**: Points where the graph intersects the x-axis. - The graph crosses the x-axis at \( x = -2 \) and \( x = 0 \). - **x-intercepts:** \( (-2, 0) \) and \( (0, 0) \). - **y-intercept**: Point where the graph intersects the y-axis. - The graph crosses the y-axis at \( (0, 0) \). ## 6. Domain - The graph extends indefinitely in both directions (as indicated by arrows). - **Domain:** All real numbers, expressed as \( (-\infty, \infty) \). ## 7. Range - The lowest point on the graph occurs at \( y = -2 \) and it increases without bound. - **Range:** \( [-2, \infty) \). ## 8. Continuous or Discrete - The graph is unbroken. - **Answer:** Continuous. ## 9. Function or Not a Function - Each x-value corresponds to only one y-value. - **Answer:** Function. --- # Complete Description Table | Property | Answer | |-------------------------|---------------------------------| | Shape | Curve | | Line of Symmetry | None | | Increasing/Decreasing | Both | | Asymptotes | None | | Intercepts | (-2, 0), (0, 0) | | Domain | \( (-\infty, \infty) \) | | Range | \( [-2, \infty) \) | | Continuous/Discrete | Continuous | | Function/Not a function | Function | --- # Final Answers (for Writing on Worksheet) - **Shape:** Curve - **Line of symmetry:** None - **Increasing or decreasing or both:** Both - **Asymptotes:** None - **Intercepts:** (-2, 0), (0, 0) - **Domain:** \( (-\infty, \infty) \) - **Range:** \( [-2, \infty) \) - **Continuous or discrete:** Continuous - **Function or not a function:** Function --- If you require any further clarification or additional details, feel free to ask!